Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
#define in std::cin
#define out std::cout
#define rep(i,N) for(int i=0;i<N;++i)
typedef long long int LL;

int main()
{
	LL N;
	in >> N;
	std::vector<long double>a(N);
	rep(i, N) in >> a[i];

	long double ans = 0;
	std::sort(a.begin(), a.end());
	rep(i, N)
	{
		for (int j = i + 1; j < N; ++j)
		{
			long double m = a[j] - a[i], u1 = 0, u2 = 0;
			for (int k = N - 1; k >= 0; --k)
			{
				if (k != i && k != j)
				{
					if (u1 == 0) u1 = a[k];
					else if (u2 == 0)
					{
						u2 = a[k];
						break;
					}
				}
			}
			ans = std::max(ans, (u1 + u2) / m);
		}
	}

	out << std::fixed << std::setprecision(6);
	out << ans << std::endl;
}